Related papers: An alternative delayed population growth differenc…
We consider a partial differential equation that arises in the coarse-grained description of epitaxial growth processes. This is a parabolic equation whose evolution is governed by the competition between the determinant of the Hessian…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
We follow up on a companion work that considered growth rates of populations growing at different sites, with different randomly varying growth rates at each site, in the limit as migration between sites goes to 0. We extend this work here…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…
In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in…
Verhulst logistic curve either grows OR decays, depending on the {\it growth rate} parameter value. A similar situation is found in the Gompertz law about human mortality. However, growth can neither be infinite nor reach a finite steady…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…
The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…
A demographic Allee effect occurs when individual fitness, at low densities, increases with population density. Coupled with environmental fluctuations in demographic rates, Allee effects can have subtle effects on population persistence…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global…